Corollary

Tag 00I1, permanent. Cite it as [Bourbaki, Tag 00I1].

Algebra, VIII, p. 280, § 15. Brauer Groups

Let A and B be central simple algebras of finite degree over K. Then A and B are isomorphic if and only if they are similar and have the same degree.

This follows from the equivalence of properties (i) and (iv) of Proposition 3 and the fact that dim $_K(\mathbf{M}_n(D)) =$ dim $_K(D)\times n^2$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Proposition 3